The Schrödinger–Langevin equation with and without thermal fluctuations

Journal Article · Sun May 15 00:00:00 EDT 2016 · Annals of Physics

DOI:https://doi.org/10.1016/J.AOP.2016.02.005· OSTI ID:22560321

Katz, R., E-mail: [e-mail]; Gossiaux, P.B., E-mail: [e-mail]

The Schrödinger–Langevin equation (SLE) is considered as an effective open quantum system formalism suitable for phenomenological applications involving a quantum subsystem interacting with a thermal bath. We focus on two open issues relative to its solutions: the stationarity of the excited states of the non-interacting subsystem when one considers the dissipation only and the thermal relaxation toward asymptotic distributions with the additional stochastic term. We first show that a proper application of the Madelung/polar transformation of the wave function leads to a non zero damping of the excited states of the quantum subsystem. We then study analytically and numerically the SLE ability to bring a quantum subsystem to the thermal equilibrium of statistical mechanics. To do so, concepts about statistical mixed states and quantum noises are discussed and a detailed analysis is carried with two kinds of noise and potential. We show that within our assumptions the use of the SLE as an effective open quantum system formalism is possible and discuss some of its limitations.

• OSTI ID: 22560321
• Journal Information: Annals of Physics, Vol. 368, Issue Complete; Other Information: Copyright (c) 2016 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA); ISSN 0003-4916
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ASYMPTOTIC SOLUTIONS
DAMPING
EXCITED STATES
FLUCTUATIONS
LANGEVIN EQUATION
MIXED STATE
MIXED STATES
POTENTIALS
QUANTUM SYSTEMS
RELAXATION
SCHROEDINGER EQUATION
STATISTICAL MECHANICS
STOCHASTIC PROCESSES
THERMAL EQUILIBRIUM
TRANSFORMATIONS
WAVE FUNCTIONS